The chiral phase transition of QED₃ around the critical number of fermion flavors

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At zero temperature and density, the nature of the chiral phase transition in QED₃ with Nf massless fermion flavors is investigated. To this end, in Landau gauge, we numerically solve the coupled Dyson-Schwinger equations for the fermion and boson propagator within the bare and simplified Ball-Chiu vertices separately. It is found that, in the bare vertex approximation, the system undergoes a high-order continuous phase transition from the Nambu-Goldstone phase into the Wigner phase when the number of fermion flavors Nf reaches the critical number Nf,c, while the system exhibits a typical characteristic of second-order phase transition for the simplified Ball-Chiu vertex.